Abelian Factor in 2-step Nilpotent Lie Algebras Constructed from Graphs
Differential Geometry
2022-12-20 v2
Abstract
We consider real 2-step metric nilpotent Lie algebras associated to graphs with possibly repeated edge labels as constructed by Ray in 2016. We determine how the structure of the egde labeling within the graph contributes to the abelian factor in these Lie algebras. Furthermore, we explicitly compute the abelian factor of the 2-step nilpotent Lie algebras associated with some families of graphs such as star graphs, cycles, Schreier graphs, and properly edge-colored graphs. We also study the singularity properties of these Lie algebras in certain cases.
Cite
@article{arxiv.2208.09541,
title = {Abelian Factor in 2-step Nilpotent Lie Algebras Constructed from Graphs},
author = {Rachelle DeCoste and Lisa DeMeyer and Meera Mainkar and Allie Ray},
journal= {arXiv preprint arXiv:2208.09541},
year = {2022}
}
Comments
Communications in Algebra (2022)